\newproblem{lay:2_1_18}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.1.18}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Suppose the third column of $B$ is all zeros. What can be said about the third column of $AB$?
}{
  % Solution
	Let us consider the different columns of $B$
	\begin{center}
	   $B=\begin{pmatrix}\mathbf{b}_1 & \mathbf{b}_2 & \mathbf{b}_3 & ... \end{pmatrix}$
	\end{center}
	The product of $AB$ is
	\begin{center}
		$AB=A\begin{pmatrix}\mathbf{b}_1 & \mathbf{b}_2 & \mathbf{b}_3 & ... \end{pmatrix}=\begin{pmatrix}A\mathbf{b}_1 & A\mathbf{b}_2 & A\mathbf{b}_3 & ... \end{pmatrix}$
	\end{center}
	If $\mathbf{b}_3=\mathbf{0}$, then
	\begin{center}
		$A\mathbf{b}_3=A\mathbf{0}=\mathbf{0}$
	\end{center}
	So, the third column is also $\mathbf{0}$.
}
\useproblem{lay:2_1_18}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
